IUCr J
ISSN 2052-2525
CHEMISTRY
j
CRYSTENGReceived 29 October 2018 Accepted 28 May 2019
Edited by M. Eddaoudi, King Abdullah University, Saudi Arabia
‡ Joint first authors.
Keywords:anti-ferroelectricity; phase transitions; symmetry-mode analysis; crystal engineering; inorganic materials; materials science; inorganic chemistry.
Supporting information:this article has supporting information at www.iucrj.org
Symmetry-mode analysis for intuitive observation of structure–property relationships in the lead-free antiferroelectric (1x)AgNbO
3–xLiTaO
3Teng Lu,a‡ Ye Tian,b,a,c*‡ Andrew Studer,dNarendirakumar Narayanan,a,dQian Li,eRay Withers,aLi Jin,bY. Mendez-Gonza´lez,fA. Pela´iz-Barranco,fDehong Yu,d Garry J. McIntyre,dZhuo Xu,bXiaoyong Wei,b* Haixue Yancand Yun Liua*
aResearch School of Chemistry, Australian National University, Canberra, ACT 2601, Australia,bElectronic Materials Research Laboratory, Xi’an Jiaotong University, Xi’an, Shannxi 710049, People’s Republic of China,cSchool of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, UK,dAustralian Nuclear Science and Technology Organisation, New Illawarra Road, Lucas Heights, NSW 2234, Australia,eAdvanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA, andfPhysics Faculty, Institute of Science and Technology of Materials, Havana University, Cuba. *Correspondence e-mail: [email protected], [email protected], [email protected]
Functional materials are of critical importance to electronic and smart devices.
A deep understanding of the structure–property relationship is essential for designing new materials. In this work, instead of utilizing conventional atomic coordinates, a symmetry-mode approach is successfully used to conduct structure refinement of the neutron powder diffraction data of (1x)AgNbO3–xLiTaO3(0 x0.09) ceramics. This provides rich structural information that not only clarifies the controversial symmetry assigned to pure AgNbO3 but also explains well the detailed structural evolution of (1x)AgNbO3–xLiTaO3(0x0.09) ceramics, and builds a comprehensive and straightforward relationship between structural distortion and electrical properties. It is concluded that there are four relatively large-amplitude major modes that dominate the distortedPmc21structure of pure AgNbO3, namely a 3 antiferroelectric mode, a T4+ aac0 octahedral tilting mode, an H2 a0a0c+/a0a0coctahedral tilting mode and a 4ferroelectric mode. The H2 and 3 modes become progressively inactive with increasing x and their destabilization is the driving force behind the composition-driven phase transition between the Pmc21 and R3c phases. This structural variation is consistent with the trend observed in the measured temperature-dependent dielectric properties and polarization–electric field (P-E) hysteresis loops. The mode crystallography applied in this study provides a strategy for optimizing related properties by tuning the amplitudes of the corresponding modes in these novel AgNbO3-based (anti)ferroelectric materials.
1. Introduction
Functional materials with (anti)ferroelectricity (AFE/FE) offer innumerable applications for sensors, actuators, memory and energy-storage devices (Liuet al., 2015; Haoet al., 2009;
Setteret al., 2006; Haertling, 1999; Damjanovic, 1998). Lead- containing materials such as Pb(Zr,Ti)O3, Pb(Zr,Sn,Ti)O3and Pb(Mg1/2Nb2/3)O3–PbTiO3 have already been manufactured into commercial devices due to their excellent properties (Park & Shrout, 1997; Bellaiche & Vanderbilt, 1999; Guoet al., 2000; Mirshekarlooet al., 2010), but environmental concerns nowadays prompt investigations into lead-free alternatives (Saitoet al., 2004; Shrout & Zhang, 2007). Recently, AgNbO3
(AN) has attracted researchers’ attention as a novel lead-free AFE material. It is reported that the recoverable energy density of pure AN ceramics can reach 2.1 J cm3. After
substituting 20% Nb5+ with Ta5+, however, the recoverable energy density doubles to 4.2 J cm3, the highest value achieved to date in lead-free AFE ceramics (Zhaoet al., 2017;
Tianet al., 2016). One of the important reasons enabling such a high energy density in AN is its ultrahigh field-induced polarization (52mC cm2), which strongly suggests that AN should remain as the basis material from which to develop lead-free alternatives with high piezoelectric performance (Fu et al., 2007, 2008, 2009, 2011a). Referring to the investigation carried out by Fu et al. (2008), Li+ doping can stabilize the ferroelectricity of AN. More importantly, the synthesized single-crystalline (Ag0.914Li0.086)NbO3 exhibits a relatively large piezoelectric coefficient with a higher Curie temperature (TC), making it a competitive candidate for new lead-free piezoelectrics.
Currently, a considerable amount of effort, especially into chemical modification, is being made to improve the energy storage and/or piezoelectric capabilities of AN-based systems (Tian et al., 2017; Zhao et al., 2018, 2016). Nonetheless, the underlying structure and structural evolution of such doped materials still remain ambiguous and controversial. From a structural point of view, many room-temperature FE and/or AFE structures exhibit at least one large-amplitude (primary) distortive mode, in addition to the fundamental FE (polar q= 0 mode) and/or AFE modes which are directly responsible for their FE and/or AFE properties, when compared with their typically higher-symmetry paraelectric phases (Dove, 1997;
Stokeset al., 1991). The traditional single soft-mode approach is unable to describe the complete structural distortion in such circumstances. In seeking to understand the competing structural instabilities underlying the behaviour of such FE and AFE phases, it is thus very useful to utilize a mode crystallography approach, whereby the primary and induced secondary modes of distortion are clearly identified via symmetry-mode decomposition (Perez-Mato et al., 2010). In such an approach, the room-temperature structure is described in terms of an undistorted parent structure and various additional distortive modes. Each mode is then asso- ciated with a specific allowed modulation wavevector and irreducible representation (irrep), as well as the mode amplitude.
This work therefore introduces this methodology into the structure refinement of neutron diffraction data collected from pure AN and associated compounds for better under- standing of the chemically induced structural evolution and property changes, and is laid out in three parts. In the first part, symmetry-mode decomposition is successfully applied to pure AN for both the non-polar Pbcm and polar Pmc21 space groups. It provides new insight into these two controversial symmetries, the origin of which will be addressed below, in terms of distortive modes. In the second part we extend the application of symmetry-mode analysis to the newly synthe- sized (1x)AgNbO3–xLiTaO3 material system (ANLT100x hereafter) to build a more precise correlation between the structure and electrical properties of the ANLT system. The latter are presented in the third part. The symmetry-mode decomposition approach shows the variation in the relative
amplitudes of the different modes as a function of the LiTaO3
dopant level, thereby enabling a better understanding of the structure of AN itself and its phase-transition behaviour under chemical modification, by comparison with conventional Rietveld fractional coordinate refinements. We believe this work not only presents a systematic investigation of a new AN-based solid-solution system, but also illustrates the influ- ence of composition on the distortive-mode amplitudes and thus on the relative properties. Such an approach can guide future work in enhancing the AFE or FE properties of AN- based materials.
2. Results and discussion
2.1. Symmetry-mode decomposition of AgNbO3
The average structure of AN at room temperature still remains controversial because either thePbcmor thePmc21
space group can be used reasonably well for structure refinement based on X-ray and neutron powder diffraction data (Sciauet al., 2004; Levinet al., 2009; Yashimaet al., 2011).
In this current work, the symmetry-mode decomposition approach is thus adopted to describe obvious differences between these two distorted structures proposed by Levinet al.(2009) and Yashimaet al.(2011), respectively, to reveal a
‘hidden structural correlation’. Note that thePbcmandPmc21
structures use different axes settings. In order to make them comparable and decomposed from the same parent structure, thePbcmstructure is transferred into aPmcastructure, based on the settings used by Yashima et al. (2011). The parent structure was then chosen as an undistortedAmmmstructure (Fig. 1), which accommodates the octahedral rotation and avoids lattice strain. The unit-cell axes relationship between this Ammm structure (subscript A) and the pseudo-cubic perovskite structure with Pm3m symmetry (subscript p) is cpaA,ap+bpbA,ap+bpcA.
Atomic displacements from the mode decomposition of the distorted Pmca and Pmc21 structures are listed in the supporting information (Tables S1 and S2). ThePmcastruc- ture is the result of irrep distortions of the Ammm parent structure associated with five different irrep modes:3, Y3, Z2, T4+ and H2. However, the associated atomic displace- ments for different modes display strong differences. Taking
Figure 1
The parentAmmmstructure viewed along (a) theaaxis and (b) thecaxis.
O3 as an example, the shift associated with the T4+ mode along the a axis is around 0.217 A˚ , while the shift resulting from the Z2mode is only 0.004 A˚ , smaller than the standard deviation for the refinement. For the polar Pmc21structure, the origin is allowed to shift along thecdirection. In this case, five more modes are allowed by comparison with the Pmca structure (Table S2), which are 4, 1, Y2+, Z3+ and H4.
Similarly, the atomic displacements associated with modes like 1 and Z2are much smaller than the associated standard deviation. For each individual mode, the dimensions indicate the number of independent components or basis modes involved, and are larger forPmc21(32) than forPmca(15).
The global amplitude, A, is calculated by ðmA2;mÞ1=2, whereA,mdenotes the amplitude for the specific component m. The dimensions and global amplitudes for each mode are listed together with the corresponding wavevectorsqin Table 1 for both distorted structures. Clearly, the T4+, H2 and 3 modes have significantly larger global amplitudes in both cases. In the following, we identify the irrep modes whose condensation leads directly to the observed distortions.
Referring to the ‘isotropy’ subgroups (Campbellet al., 2006), the primary modes usually have the larger amplitudes. For Pmcasymmetry, any two of the3, T4+ and H2 modes could result in the observed distortions. Taking the relative ampli- tudes into consideration, we identify T4+ and H2 as the most important primary modes. Referring to the wavevectors listed in Table 1, the 3 mode can therefore be assigned to a secondary mode induced by the two most important co- existing primary T4+ and H2 modes, i.e. q2 = q7 q8. However, for the lowering of the symmetry to Pmc21, the condensation of the T4+ and H2 modes is insufficient. To obtain this structure another primary mode is required, namely the 4 mode at the zone centre with a relatively large amplitude. ThePmc21structure can then be considered as a subgroup of thePmcastructure. Therefore, we will focus on the four main modes T4+, H2,3 and 4step by step to understand the structural origin of the properties observed in silver niobate.
Figs. 2(a) and 2(b) show the distorted AN structure induced by the addition of the T4+ mode only to theAmmm parent
structure. Thisq7= [1/2 1 0]* T point mode occurs at the first Brillouin-zone boundary of its parentAmmm structure. The displacements involved correspond to a pure R(h110ip)-type octahedral rotation around the c = cA ap+ bpaxis, i.e.
aac0 octahedral tilting in Glazer notation (Glazer, 1975).
Figs. 2(c) and 2(d) show the distorted structure induced by the q8= [1/4 1 0] (equivalent to [1/2 1/2 1/4]p*) H2 mode, which also occurs at the Brillouin-zone boundary and is also asso- ciated with octahedral rotation, but this time around thea= 4aA = 4cp axis. The H2 mode thus exhibits R(h001ip)-type octahedral rotation,i.e.rotation around theaaxis, but not in the usual in-phase or antiphase rotation patterns expected for perovskites. If the structure is viewed alonga[Fig. 2(c)], it can be seen that the NbO6octahedra are antiphase tilted. In fact, this is because the adjacent NbO6octahedra rotate alternately in a single column along theaaxis [Fig. 2(d)]. If the ‘+’ sign denotes that the octahedron rotates clockwise and the ‘’ sign denotes anticlockwise rotation viewed along a, the NbO6
octahedra [the right-hand column in Fig. 2(d)] rotate in the form of ++ around theaaxis, ora0a0c+/a0a0c. In other words, if the adjacent octahedra with in-phase tilt are regarded together as one unit, the dashed red lines in Fig. 2(d) can be considered as antiphase boundaries between these units.
When combined with the T4+ mode, the resultant distorted structure is an aac+/aac tilting system, close to the reported abc+/abc. In fact, Yashima et al. (2011) suggested equal tilting angles along [100]p and [010]p, i.e.
abc+/abc=aac+/aac.
The T4+ and H2 modes together construct the overall octahedral tilting system in AN. It is worth noting that the octahedral tilting involves oxygen displacements and the Table 1
The dimensions and global amplitudes of distortive modes observed in thePmcaandPmc21structures.
The q vector basis refers to the Ammm and pseudo-cubic perovskite structures.
Wavevectorq Dimension A(A˚ )
Ammm Pseudo-cubic qi Irrep Pmca Pmc21 Pmca Pmc21
[0 0 0]* [0 0 0]p* q0 4 5 0.21
[1/4 0 0]* [0 0 1/4]p* q1 1 4 0.09
[1/4 0 0]* [0 0 1/4]p* q2 3 5 5 0.48 0.47
[0 1 0]* [1/2 1/2 0]p* q3 Y2+ 2 0.17
[0 1 0]* [1/2 1/2 0]p* q4 Y3 3 3 0.16 0.16
[1/2 0 0]* [0 0 1/2]p* q5 Z3+ 2 0.03
[1/2 0 0]* [0 0 1/2]p* q6 Z2 2 2 0.04 0.02
[1/2 1 0]* [1/2 1/2 1/2]p* q7 T4+ 3 3 1.23 1.22 [1/4 1 0]* [1/2 1/2 1/4]p* q8 H2 2 2 1.00 0.97
[1/4 1 0]* [1/2 1/2 1/4]p* q9 H4 4 0.11
Figure 2
(a), (b) The distorted AN structure induced by the T4+ mode only, viewed along (a) thecaxis and (b) theaaxis. (c), (d) The distorted AN structure induced by the H2 mode only, viewed along (c) theaaxis and (d) thebaxis. The +/signs on the right in panel (d) show the clockwise/
anticlockwise rotation, respectively, of the right-hand column of octahedra around theaaxis. (e) The distorted structure induced by the 3 mode only, and (f) that of the 4mode only. The black arrows in panel (e) show the off-centre Nb5+and Ag+cation displacements, while the red arrows in panels (e) and (f) indicate the local spontaneous polarization. The horizontal dashed red lines represent antiphase boundaries for octahedral rotation around theaaxis in panel (d) and cation displacements along thecaxis in panel (e).
mode amplitude is given in a˚ngstro¨ms. The larger amplitude corresponds to a larger distortion. Furthermore, we will also include the tilting angles separately from the mode amplitude to describe the octahedral tilting fully. As mentioned above, the primary T4+ and H2 modes can directly produce a resul- tantPmcastructure.
The distortive structure induced by the next-strongest (induced secondary) 3 mode is shown in Fig. 2(e) and is mainly related to cation atomic displacements. Within one unit [two octahedral layers thick, shown between two dashed red lines in Fig. 2(e)], the Nb2 and Ag3 atoms are displaced off- centre along c [as shown by the black arrows in Fig. 2(e)], while anions such as O6, O7 and O5 are displaced to a lesser extent in the opposite direction. In this two-layer unit, the displaced ions would generate spontaneous polarization along +c, as shown by the red arrow. In the adjacent two-layer unit alonga, cations such as Nb1 and Ag2 are displaced alongc, while O2, O3 and O4 again move in the opposite direction, forming an overall dipole moment along c. Note that the Ag1 and O1 ions are located at the boundary between adja- cent two-layer units and are thus not allowed to move along thecaxis as a consequence of a required symmetry operation.
Note that the dipole moment formed within each unit has the same magnitude, but the direction switches 180from one unit to the next, resulting in an antiparallel dipole alignment. In other words, the3 mode contributes directly to the observed antiferroelectricity in AN. Intriguingly, the two-layer units drawn in Figs. 2(d) and 2(e) show the same behaviour. After crossing each antiphase boundary, both the octahedral rota- tion around theaaxis [in the case of Fig. 2(d)] and the dipole moment [in the case of Fig. 2(e)] change their sign. Consid- ering 3 as an induced mode, it is evident that the anti- ferroelectric alignment in AN is very closely related to the observed a0a0c+/a0a0c (or ++ ) octahedral rotation pattern.
Finally, the distortive structure associated with the zone- centre 4 mode only, which, as a primary mode, differ- entiates the Pmc21 structure from thePmca structure by an additional ‘softening’, is shown in Fig. 2(f). For this ferro- electric q= 0 distorted structure, all ions move along thec direction but with different magnitudes. For the cations, the displacements of Ag1, Ag2 and Ag3 (0.002 A˚ ) are much smaller than those of Nb1 and Nb2 (0.059 A˚ ). For the anions, the apical oxygens, i.e. O1, O2 and O5, are displaced by 0.025 A˚ , while the equatorial O3, O4, O6 and O7 anions are displaced by 0.027 A˚ . As a result, the spontaneous polariza- tion points alongc. This 4mode is therefore the origin of the weak ferroelectricity previously observed in silver niobate under a low electric field (E field) (Fu et al., 2007).
Undoubtedly, both the AFE3 mode and the FE 4mode respond to an externally applied E field, but the global amplitude of the FE mode is less than half that of the AFE mode. The competition between these two modes thus results in the observed ‘ferrielectricity’ (Yashimaet al., 2011), and also explains the appearance of a non-zero remnant polarization (Pr) observed in the doubleP-Ehysteresis loop of AN.
2.2. Symmetry-mode refinement
In the previous section, we gave a detailed description of the condensation of the various symmetry modes, resulting in the two different space groups and structures reported for AN.
In this section, we apply the above relationships to the ANLT100x series of samples for a systematic study of the variation in the modes by a mode-refinement procedure, which was conducted using theFULLPROFsuite (Rodrı´guez- Carvajal, 1993) in conjunction withISODISTORT(Campbell et al., 2006). In contrast with conventional Rietveld refine- ment, the refinement of distortive modes enables a reasonable approach to refining the distorted structures,e.g.the primary modes should be refined first and modes with large amplitudes given higher priority. The reference structure was chosen to be the distorted perovskite-type structure with Pmc21 space- group symmetry. This is due to the fact that both convergent- beam electron diffraction (CBED) and selected-area electron diffraction (SAED) prove the existence of a polar structure on the local scale (Tian et al., 2016; Yashima et al., 2011).
Furthermore, as described in the previous section, thePmc21
structure exhibits an additional primary mode, the 4mode, which explains the observed weak ferroelectricity in a lowE field. It is thus more reasonable to investigate its variation as a function of LiTaO3 content. A systematic correlation of this mode with the ferroic properties may solve the apparent puzzle regarding the room-temperature AN structure.
Fig. 3(a) shows the neutron powder diffraction (NPD) data of pure AN collected in the 2range of 22–116, while Figs.
3(b) and 3(c) show selected reflections associated with the T4+, H2 and 3 modes. It is clear that the symmetry-mode refinement approach provides detailed information about the reflection intensities associated with the different modes. For example, the reflections around 2= 41.5 and 55are induced by the T4+ mode, related to the antiphase NbO6 octahedral rotation around [110]p. Additionally, the reflections around 39.8 and 59.5can be attributed to the combination of the3 and H2 modes, with their intensities mainly determined by the H2 mode as a result of its larger global amplitude.
ThePmc21single-phase model was also attempted on NPD patterns of other ANLT100xsamples. Given the relatively low
Figure 3
(a) Rietveld symmetry-mode refinement based on thePmc21space group with the neutron powder diffraction (NPD) data of AN at room temperature. (b), (c) Selected reflections associated with the T4+, H2 and 3 modes.
doping level (<10%), the Li+ and Ta5+ ions are fixed at the same positions of Ag+and Nb5+, respectively. For samples with relatively small x values,e.g. x= 0.03 and 0.045, the Pmc21
single-phase model leads to a reasonable refinement result [Figs. 4(a) and 4(b)]. However, forx= 0.053, thePmc21single- phase model fails to fit the experimental data well [Fig. 4(c)]
and a large divergence is especially observed in the 2range of 70 to 80. The insert plot indicates that the selected peaks are poorly fitted. Referring to the pseudo-cubic perovskite struc- ture (subscript p), it is found that the largest difference appears in calculating parent reflections such ash220ip* and h221ip*. For example, the intensity ratio of the split [220]p*/[202]p* reflections is incorrectly estimated. Further- more, the intensity of the 1/2h531ip* reflection, determined by the amplitude of the T4+ mode, is underestimated. Interest- ingly, the calculated intensities of reflections associated with the 3 and H2 modes are in good agreement with the experimental data.
A bond-valence sum (BVS) calculation (Brown, 1981) suggests that the substitution of Ta5+for Nb5+does not make a big difference, but the replacement of an Li+ion for an Ag+ ion would strongly destabilize the parent AN structure.
Previous studies of Li-doped AgNbO3systems (Fuet al., 2008, 2011b; Khanet al., 2012) also reported that, with higher Li+ content, the average structure is transformed into a rhombo- hedral phase and the properties change accordingly. Intui- tively, the features of the underestimated reflections in Fig.
4(c) are consistent with the patterns induced by the presence of anR3csymmetry structure. A two-phase model refinement (space groups Pmc21 and R3c) was thus applied to the ANLT5.3 pattern, which evidently improved the refinement quality [Fig. 4(d)].
For theR3cphase, the symmetry-mode decomposition has been done with reference to the reported high-temperature cubic structure of AN [Pm3m symmetry, ICSD (Inorganic Crystal Structure Database, http://www2.fiz-karlsruhe.de/
icsd_home.html) refcode 55649] (Sciauet al., 2004). The basis of this distorted structure is set as:arap+cp,brbpcp
andcr 2ap+ 2bp+ 2cp. For theR3cstructure, condensation of two primary modes with large amplitudes, namely 4qr0= [0 0 0]p* and R4+qr1= [1/2 1/2 1/2]p*, will lead to the observed distortions. The 4qr0= [0 0 0]p* mode, which allows off- centre ionic shifts along the c axis (the [111]p direction), contributes to the FE spontaneous polarization. The R4+qr1= [1/2 1/2 1/2]p* mode, on the other hand, is associated with antiphase octahedral rotation around the [111]pdirection,i.e.
aaaoctahedral tilting in Glazer notation (Glazer, 1975).
With further doping of LiTaO3,i.e. x = 0.06 and 0.09, the features associated with theR3cphase become more obvious.
As shown in Fig. 5(a), theh111ip* reflections contain a small shoulder at the lower 2angle which does not belong to the Pmc21phase. The two-phase model was also applied to refine the data of both ANLT6 and ANLT9 (Fig. 5), resulting in good agreement between the observed and calculated patterns. It should be noted that both the T4+ mode for thePmc21phase and the R4+ mode for the R3c phase contribute to the intensities of theGp[1/2 1/2 1/2]p* reflections, so both irrep notations are labelled. For x = 0.09, an additional peak observed at 26 [Fig. 5(b), labelled by the red rectangular symbol] is probably from an impure LiNbO3 phase as Figure 4
Rietveld symmetry-mode refinement of the NPD data of ANLT100x, (a) x= 0.03, (b)x= 0.045 and (c)x= 0.053 with a space group ofPmc21, collected at room temperature. (d) Rietveld symmetry-mode refinement of the NPD pattern of ANLT5.3 in terms of the two-phase model (R3c+ Pmc21). The insert plots in panels (c) and (d) are enlargements of selected reflections, indexed by the related irrep modes.
previously reported (Khan et al., 2012). Note that due to overlapping, peak intensities are easily influenced by cross- talk. Furthermore, the BVS calculation indicates that Li+ would prefer to move away from the Ag site to an interstitial site (Alonso et al., 2000; Brant et al., 2012). Therefore, the reliability factors of the refinement on ANLT9 are not as good as those for the lower-level LiTaO3doped samples (Table S3).
Due to the detection of a secondary phase, a deviation in x from 9% for LiTaO3 is probably expected. The refinement results reveal that the molar fraction of this secondary phase is around 2.5%, suggesting that the dopant level of LiTaO3is around 6.5%. Application of the modified composition did indeed improve the reliability factors (Rpchanges from 0.0268 to 0.0260). Therefore, in the following we assume a LiTaO3
content of 6.5% for ANLT9 in order to guide the reader’s understanding of the structural evolution as a function of LiTaO3content. Details of the refined atomic positions of the ANLT100x system are shown in the supporting information (Tables S4–S9).
Fig. 6 shows the structural evolution of the ANLT100x materials as a function of LiTaO3content. In thePmc21single- phase region,i.e. x< 0.053, the unit-cell parameters (a,band c) decrease gradually with respect to the xvalue [Fig. 6(a)].
This shrinkage of the unit cell is possibly due to the intro- duction of Li+, whose ionic radius is 92 pm compared with the 128 pm radius of Ag+(Shannon, 1976). When theR3cphase appears (at x = 0.053), thea, b andc values for the ortho-
rhombic phase exhibit a slight increase. In the two-phase region,i.e. x 0.053, with further doping the lattice parameter aincreases, whereasbandcdecrease. On the other hand, the fraction of theR3cphase increases from 12.1 to 53% for 0.053 x0.06. For theR3cphase, bothaandcare reduced with increasing x [Fig. 6(b)]. The variation in the unit-cell para- meters of both thePmc21andR3cstructures cannot simply be explained by the ionic radii; it is probably linked to octahedral rotation and interaction between the two phases.
Fig. 6(c) shows the global amplitude (A) of the main modes changing as a function of LiTaO3content for both thePmc21
and R3c phases. Larger A values imply larger atomic displacements and a more highly distorted structure. In the Pmc21 phase, referring to the mode decomposition in pure AN, the four critical modes can be divided into ionic displa- cements (FE 4and AFE3) and octahedral rotations (H2 and T4+). The amplitudes of the H2 and3 modes decrease upon Li+doping. However, the slope has an inflexion point at x= 0.053 and descends rapidly upon further Li+doping. The amplitude of the FE 4mode, on the other hand, displays the opposite trend to that of the AFE3 mode. It is note- worthy that the deviation of the 4 mode’s amplitude becomes quite large when x 0.053, indicating that the variation of this parameter has less impact on the refinement results.
In Section 2.1 we described the distorted structure induced by the largest-amplitude single modes, and also found that the overall octahedral tilting pattern is induced by a combination of T4+ and H2 modes. Instead of the related oxygen displacements, the tilting angles can also be used to reflect the Figure 5
Plots of NPD data with Rietveld analysis for (a) ANLT6 and (b) ANLT9.
The insert plots at the top right are enlargements of selected regions. The insert plot with a red frame on the left of panel (b) is an enlargement showing the presence of an impure LiNbO3phase.
Figure 6
(a) Refined lattice parameters of thePmc21phase and the phase fraction of theR3cphase. (b) Lattice parameters of theR3cphase. (c) The global amplitudes of the main modes in both the Pmc21 and R3c phases, changing as a function of LiTaO3content.
degrees of distortion for these octahedral rotation modes. As shown in Fig. 7(a), the structure induced by the T4+ mode can be visually expressed by the tilting angles between the two adjacent NbO6octahedra viewed along either [100]por [010]p. Here, O1 and O2 (subscript O denotes the orthorhombic phase) are used to illustrate the tilt angles. If there is no octahedral distortion, O1= O2. The H2 mode is associated with the in- or antiphase rotation around [001]p and O3 is used to characterize the tilting angle for this mode [Fig. 7(b)].
In theR3cphase, the R4+ mode denotesaaaoctahedral tilting, and therefore the tilt angle along anyh100ipdirection,
R1(subscript R denotes the rhombohedral phase), is used to describe this distorted structure [Fig. 7(c)]. Fig. 7(d) shows the quantitative analysis of these rotation angles. For O1 and
O2, they are almost equivalent when x 0.053, and both increase slightly as the doping level increases. Whenx 0.053,
O1and O2behave differently: O1increases, whereas O2
decreases. This suggests that the octahedral distortion is accompanied by the appearance of the R3c phase. Further- more, the decrease in O2 also explains the increase in the unit-cell parameter a for x 0.053. The tilt angle R1
increases with increases in the heavily underbonded Li+ dopants. For the H2 mode, O3decreases slightly before the appearance of theR3cphase and then sharply when theR3c phase dominates the samples. This behaviour is very similar to that of primary modes that vary as a function of temperature in other materials (Khalyavin et al., 2014; Faik et al., 2012;
Go´mez-Pe´rezet al., 2016). Therefore, the destabilization of the H2 mode is very important to this composition-driven phase transition in the ANLT100xsystem.
Note that the sudden drop in O3is deduced by the change in the degree of ordering of a0a0c+/a0a0coctahedral tilting.
This is probably due to the fact that the rotation around [001]p
creates differing periodicities or is totally disordered (Khanet al., 2012; Wanget al., 2011; Guo et al., 2011; Liuet al., 2012;
Bellaiche & I´n˜iguez, 2013; Prosandeev et al., 2013), i.e. the associated modulation wavevector moves along the H line in
the first Brillouin zone of the parentAmmmstructure. In the Li-doped AgNbO3material system (Khanet al., 2012, 2010), electron diffraction patterns showGp[1/2 1/2 1/3]p* satellite reflections, which in turn indicate a movement to the zone boundary (T point) of the H2 mode. Finally, the combination of the T2+ (a0a0c) and T4+ modes induces the aaa octahedral tilting observed in theR3cphase, and therefore the variation in the H2 mode locally builds an intermediate structure between thePmc21andR3cphases.
As mentioned above, the 4 mode is responsible for ferroelectricity in both thePmc21 andR3c phases, while the 3 mode is associated with antiferroelectricity for thePmc21
phase. Note that the3 mode can be regarded as a secondary mode induced by primary H2 and T4+ modes, and its composition-dependent amplitude follows the same trend as the H2 mode, suggesting an improper AFE nature of AN (Bellaiche & I´n˜iguez, 2013).
In order to analyse the (anti)ferroelectricity further, the ionic displacements associated with the different modes are extracted and plotted as a function of composition in Fig. 8.
Although some atomic displacements along the b axis are involved in both 4 and 3 modes in the Pmc21 phase (Table S2), the refined values are quite small. Furthermore, because the (anti)parallel dipole moments are aligned along the c axis, only displacements from the z coordinates are considered. For the 4mode in thePmc21phase [Fig. 8(a)], dO2O1 (displacement of the apical oxygen), dO3O1
Figure 7
The distorted structure induced by (a) the T4+ mode for thePmc21phase viewed along thebpaxis, (b) the H2 mode for thePmc21phase viewed along thecpaxis and (c) the R4+ mode for theR3cphase viewed along thecpaxis. (d) The LiTaO3content-dependent rotation angles.
Figure 8
The distorted structure induced by (a) the 4mode and (b) the3 mode for thePmc21phase, viewed along thebaxis. The red solid lines indicate the z coordinates for the undistorted structure, the vertical dashed red lines in panel (b) show the boundaries of the two-layer octahedral units within which the dipole moments share the same direction, and the red arrows denote the displacements of the respective ions. (c) The distorted structure induced by the 4mode for theR3c phase, viewed along the baxis. (d), (e), (f) The ionic displacements induced by (d) the 4mode, (e) the3 mode in thePmc21phase and (f) the 4mode in theR3cphase as a function of LiTaO3content.
(displacement of the equatorial oxygens),dAgO1(Ag/Li) and dNbO1(Nb/Ta) denote the ionic displacements alongcfrom the undistorted position (subscripts O and 1 indicate the orthorhombic phase and the 4 mode, respectively). Fig.
8(b) gives a schematic description of the ionic displacements associated with the3 mode. As the dipole moments exhibit antiparallel alignment with the same amplitude, only atoms involved in one unit are extracted (subscript 2 denotes the3 mode). In this case, only the displacements of Ag/Li2 (dAgO2), Nb/Ta1 (dNbO2), apical oxygen (dO2O2) and equatorial oxygen (dO3O2) are extracted. Similarly,dAgR1(Ag/Li) and dNbR1(Nb/Ta) are used to describe the ferroelectricity in the R3cphase [Fig. 8(c)]. Note that in theR3cphase, thezcoor- dinate of the oxygen is fixed to zero, therefore cationic shifts are enough to describe the spontaneous polarization.
It is interesting that, even though the amplitude of the 4 mode in the Pmc21phase exhibits a systematic increase as a function ofx, the change in bothdO2O1anddNbO1indicates that spontaneous polarization does not follow the same trend, especially whenx 0.053 [Fig. 8(d)]. The zone-centre mode is very hard to calculate accurately via powder diffraction. The large deviations suggest that the structure models based on both Pmc21 and Pbcm reproduce the experimental pattern reasonably well. By contrast, the refined values of dO2O2, dO3O2, dAgO2 anddNbO2 involved in the3 mode change systematically as a function of LiTaO3 content [Fig. 8(e)].
Before introducing the LiTaO3, the cations and anions are displaced in opposite directions,i.e. dO2O2anddO3O2< 0, and dAgO2 and dNbO2 > 0, leading to a strong spontaneous polarization within any one two-octahedral-layer unit. With increasingx, the displacements of the anions and cations begin to converge, until a sudden change occurs at x’0.053. This behaviour suggests that the dipole moment in each sublattice becomes smaller,i.e.the antiferroelectricity is weakening. For x 0.053, theR3c phase emerges and its fractional content rises with further increase inx, whereas the diminishingPmc21
phase is simultaneously accompanied by a weakening anti- ferroelectricity. As a consequence, the ferroic properties are expected to be dominated by the R3cphase in this composi- tion region. As shown in Fig. 8(f), for the sample with the largest R3c phase fraction (x 0.06), dAgR1 remains unchanged whiledNbR1shows a slight decrease.
2.3. Electrical properties
Fig. 9 shows the temperature-dependent dielectric spectra of ANLT100xbulk ceramics. That for pure AN contains three evident dielectric constant peaks, TI (70C), TII (270C) andTIII(350C), in the measured temperature range from 150 to 480C, consistent with the previously reported experimental results (Fu et al., 2007). In this temperature range, AN is reported to contain six phases: M1, M2, M3, O1, O2 and T. The M1, M2 and M3 phases have orthorhombic structures (the M label denotes the monoclinic distortion of the primitive unit cell) and all of them exhibit anti- ferroelectricity (Ratusznaet al., 2003; Kania, 2001). The peaks at the TI and TII points are assigned to the M1–M2 and
M2–M3phase transitions, respectively. The sharp peak at the TIII point is attributed to the phase transition between the AFE M3phase and a paraelectric O1phase with a space-group symmetry ofCmcm. Previously, the average structures of the M1, M2 and M3 phases were all assigned to the samePbcm space-group symmetry. The phase transitions between the three phases were interpreted as cation displacements (Levin et al., 2009, 2010; Krayzman & Levin, 2010). The broad TII
peak was proved to be the result of Nb5+ displacement dynamics, while the origin of the frequency-dependentTIpeak is still under debate (Levin et al., 2009). Recently, the TI- related peak was explained as being due to the disappearance of weak ferroelectricity within the recently proposed polar Pmc21phase,i.e.the softening of the above-mentioned 4 mode (Manishet al., 2015).
The temperature-dependent dielectric spectra of ANLT3 and ANLT4.5 [Figs. 9(b) and 9(c)] are quite similar to pure AN, again accompanied by three dielectric peaks atTI,TIIand TIII. Interestingly, the TI peak shifts gradually towards low temperature with increasing concentration of LiTaO3and, at the same time, the refined 4mode at room temperature becomes unstable. Furthermore, the increase in LiTaO3
content also shifts theTIIpeak to lower temperature with a larger dielectric constant. As mentioned above, the M3–M2
phase transition has been associated with differing degrees of order for the Nb ions. Referring to the results of Levinet al.
(2009), ordered octahedral tilting will promote the long-range order of the Nb displacements. From our experimental data, the H2 mode drops slightly with increasing x (x 0.045), which possibly suggests that the octahedral tilting becomes disordered. Therefore, this order–disorder transition can be activated at a lower thermal energy with increasing dopant concentration, thereby moving the transition point towards lower temperature. With further increases inx, an additional dielectric peakTUis first observed around 140C in ANLT5.3 and becomes dominant in the ANLT6 and ANLT9 spectra.
Figure 9
Temperature-dependent dielectric spectra for (a) AN, (b) ANLT3, (c) ANLT4.5, (d) ANLT5.3, (e) ANLT6 and (f) ANLT9 bulk ceramics.
After the appearance of the TU peak, the TI, TII and TIII
related dielectric peaks become systematically more blurred with increasing x and almost unobservable in the dielectric constant spectra of ANLT9, although there are still traces in the dielectric loss spectra. The appearance of theTUpeak is quite consistent with the results in the Li-doped AgNbO3
material system and this dielectric anomaly is clearly related to the phase transition between theR3cFE and AFE phases (Fu et al., 2011b). Therefore, the variation in the TU peak as a function ofxcan be well explained by the growth in the phase fraction of theR3cphase in the ANLT100xmaterial system.
Fig. 10 shows the polarization–electric field (P-E) hysteresis loops of ANLT100xbulk ceramics. Pure AN presents a double P-E hysteresis loop with an induced polarization of 41mC cm2under an applied field of 175 kV cm1. The critical E field (EF) to induce the FE state at 1 Hz is around 125 kV cm and the non-zero remnant polarization (Pr) is around 6mC cm2 after withdrawal of the E field. These results are almost identical to those reported earlier by Fuet al.(2007). The observedP-Ehysteresis loop confirms the AFE nature of AN, accompanied by weak ferroelectricity. Similar to pure AN, a double P-E hysteresis loop is also obtained for ANLT3 [Fig. 10(a)] butEFdecreases to 100 kV cm1and non- zero Pr to 14mC cm2. The decrease in the critical field indicates the decreasing energy barrier between the AFE and the induced FE state with increasingx. This is consistent with the gradual decrease in the mode amplitude of the3 mode as a function ofx. The AFE feature,i.e.the doubleP-Ehysteresis loop, disappears experimentally at a composition of ANLT4.5.
Instead, a highly saturated single hysteresis loop is observed with a maximum polarization (Pm)’42mC cm2and aPr’ 36mC cm2when a cycledEfield of 100 kV cm1is applied.
With a further increase in x, the ANLT100xsamples exhibit typical FE features and bothPmandPrdecrease slightly. For samples showing two-phase coexistence (x 0.053), the FE properties seem to be determined by the 4mode in theR3c phase. Intriguingly, with a further increase in the nominal x value, the amplitude of the 4mode, i.e.the spontaneous polarization, decreases.
The NPD pattern and temperature-dependent dielectric spectrum of ANLT4.5 suggest that the pristine sample contains a single AFE phase, but itsP-Ehysteresis loop shows
an FE nature [Fig. 10(a)]. In order to understand the AFE/FE behaviour observed in the ANLT100x system, the P-E hysteresis loops measured in the first and second cycles are displayed in Fig. 11. It is evident that the polarization of ANLT4.5 increases abruptly after the first quarter E field cycle, and after that theP-Eloop behaves like that observed in a classical FE material. This is very similar to the irreversibleE field-induced AFE–FE phase transition observed in PbZrO3- based AFE materials (Lu et al., 2017; Guo & Tan, 2015).
Furthermore, the EF for ANLT4.5 is around 90 kV cm1, presenting a further decrease compared with that observed for ANLT3. Forx 0.053, the steep increase in the polarization is hardly observed, and instead the polarization rises gradually over the first quarter cycle. After the first quarter cycle (same amplitude), the Pr values of ANLT5.3, ANLT6 and ANLT9 are around 13, 17 and 20mC cm2, respectively. Furthermore, after the second cycle, thePrvalues of ANLT5.3 and ANLT6 show a slight increase, while that of ANLT9 remains almost constant.
The evolution of the measured electrical properties in the ANLT100x series can be well understood from a structural viewpoint and is summarized in Fig. 12. For the pure AN sample, the distorted structure is dominated by two octahedral tilting modes (T4+ and H2), but the secondary3 AFE mode still has a relatively large mode amplitude. Thus, a character- istic doubleP-Ehysteresis loop is obtained. Upon increasing the content of LiTaO3, the H2 mode, i.e. the a0a0c/a0a0c+ octahedral tilting mode, becomes destabilized due to the heavily underbonded Li+ions and the associated AFE mode is simultaneously damped. The antiferroelectricity hence becomes weak and a lowerEfield is able to trigger an AFE–
FE phase transition. Upon further increasing xto 0.053, the rhombohedral R3c phase appears and, at this stage, the samples contain bothPmc21andR3cphases. The coexistence of the two phases implies a relatively flat energy landscape Figure 10
Room-temperature P-E hysteresis loops for (a) AN, ANLT3 and ANLT4.5, and (b) ANLT5.3, ANLT6 and ANLT9 bulk ceramics measured at 1 Hz.
Figure 11
P-Eloops for (a) ANLT4.5, (b) ANLT5.3, (c) ANLT6 and (d) ANLT9 measured at 1 Hz in the first cycle (red) and second semi-cycle (blue).
connecting thePmc21andR3cstructures. Therefore, as shown by the different P-E behaviour measured in the first and second cycles, although the virgin state of the sample has an AFE nature, the FE state will be stabilized after applying anE field. As theR3c phase fraction increases, the samples’ anti- ferroelectricity is further weakened. After applying a first- cycle E field with the same amplitude, ANLT9 exhibits the largest remnant polarization.
3. Conclusions
A symmetry-mode decomposition of AgNbO3 identifies the differences between the Pbcm and Pmc21 structures. Both distorted structures share three main modes (T4+, H2 and3) with large amplitudes. The only difference between thePbcm andPmc21structures is the ‘softening’ of the zone-centre 4 mode, which lowers the non-polarPbcmsymmetry structure intoPmc21symmetry and is regarded as the origin of the weak ferroelectricity observed in AgNbO3. Upon doping LiTaO3
into AN, the H2 mode associated with in- or antiphase octa- hedral tilting around [001]p gradually becomes destabilized, while another octahedral rotation mode (T4+,aac0tilting) shows no such significant variation. The secondary3 mode (induced by the two octahedral rotation modes) controls the antiferroelectric behaviour observed in the samples, which is then damped as a result of the H2 mode destabilization. With further LiTaO3 doping, another R3c phase appears and the samples contain two phases, suggesting a low energy barrier between the Pmc21 and R3c structures. Considering the octahedral tilting modes in both phases, we postulate that the disappearance of the H2 mode as a function of increasingxis the main force driving the structural evolution of the ANLT100x material system. More importantly, through symmetry-mode analysis this work provides a detailed physical picture of the phase transition in the ANLT100x system and builds an intuitive connection to the obtained electrical properties. We believe that this work provides
insight into how to tune the electrical properties by controlling the amplitudes of the relative modes in these antiferroelectric and ferroelectric materials. It also introduces a novel approach to structure refinement that provides information on the hidden structural correlations for a better understanding of the materials’ physical properties.
Acknowledgements
The authors thank the Australian Nuclear Science and Tech- nology Organisation for support in the form of beam time.
Funding information
T. Lu and Y. Liu acknowledge the Centre of Excellence for Integrative Brain Function of the Australian Research Council (ARC) for financial support in the form of a Discovery Project (DP160104780). This work was also supported by the International Science and Technology Cooperation Program of China under grant No.
2015DFA51100.
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